Mirror-time diffusion discount model of options pricing

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Levin, Pavel
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Abstract
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The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution, correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S&P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters.
Comment: 22 pages, 3 figures
Keywords
Quantitative Finance - Pricing of Securities, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Physics - Physics and Society
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